We define \(\mathrm {GL}^{+}(n,\mathbb {R}):=\lbrace A\in \mathbb {R}^{n\times n}|\det A>0\rbrace \) . From [1]}, \(\mathrm {GL}^{+}(n,\mathbb {R})\)  is path-connected. For all \(l=1,2,\ldots ,L\) , there exists \(Q^{(l)}\in C([0,1];\mathbb {R}^{n\times n})\)  such that
\(Q^{(l)}(0)=P^{(l)},\quad Q^{(l)}(1)=P^{(l+1)},\quad \mathrm {and}\quad \det Q^{(l)}(s)>0,\) 
